This will depend upon a lot of factors. First lets talk about when it taste best. I have a Korean friend who will only eat fresh Kimchi. He does not like any sour foods.

If Kimchi is stored correctly it will last a long time. Recently I made Kimchi Jjim using kimchi that was over a year old. This dish blew my wife away.

Some restaurants in Korea make kimchi jjigae with three year old kimchi. To store Kimchi that long it needs to be close to frezzing but not frozen. You want the microbs to eat slowly.

What I have found with kimchi is this:
Kimchi will have a very nice fresh taste for a few days. Then it starts to take on sour notes at about day three or four.
After about a week or two the fresh taste is almost gone.
After about three months it is sour and good for kimchi jjigae. (Soon after this it usually disappears.)
When my wife hides some After about six months the sourness level goes down but a well rounded sourness starts to develop.
After a year yes it is very sour but it is not a sharp sour. I can’t expalin it, you just have to try it.